eevee smoke/volume not being occluded
You can try this file (2.93) or try with some new file to eliminate something specific to your issued file.
Left Smoke sim / Right only Volumetric material ... both seems to be working.



Edit
That was real issue hunting ... the main reason is this Question ... for Eevee it is too small step in depth when volumetric is calculated. And I'm not sure there would be solution for you. Here is example with solved issue ...



... but the only one solution I found ... crop the area under Render Properties &gt; Volumetrics &gt; Start/ End and increase Samples up to 256 ... also don't use Distribution around 1, use some low value.

That means very limited range of volumetric effect depend on Camera distance.
Your file has other things that can cause some issues ... like extremely high Viewport Clip End that generates flickering, some of your objects like unicorn's hair use wrong Normals direction, and it is always better to have Applied Scale for all objects if possible ... not the case for volumetric issue, but any time I tried to switch to Eevee all computer crashed that never happened for many years to me.
Here is a file in condition that I expected you will share (hair+horn) that takes only 0.6 MB.

If you are looking for just an effect like glowing horn, you can use new object type Volume with Mesh to Volume modifier instead of Smoke simulation ... or even easier animate emission material for horn with some high value and enable Bloom in Render Properties.